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Thus, we seek to solve
\begin{displaymath} E_{xx} + g(E) = 0 \end{displaymath} (20)

on the interval $0<x<L$ and subject to boundary conditions $E_x(0) =0$ and $E_{x}(L) = -\alpha E(L)$ where $\alpha >0$, where
\begin{displaymath} g(E) = {\delta\over 1-\rho}(A^{-1}(E) -E) - k_EE. \end{displaymath} (21)

Figure: Plot of the ``function'' $g(E) = {\delta\over 1-\rho}(A^{-1}(E) -E) - k_EE$ for $ K_A = 1.0, V_A = 1.0, A_0 = 0.05, \delta = 0.1, \rho = 0.3, k_A = 0.2, k_E = 0.1$.
\begin{figure} \epsfxsize =4in \centerline {\epsffile{gu.ps}}\end{figure}

Figure: Plot of the ``function'' $g(E) = {\delta\over 1-\rho}(A^{-1}(E) -E) - k_eE$ for $ K_A = 1.0, V_A = 1.0, A_0 = 0.05, \delta = 0.1, k_A = 0.2, k_E = 0.1$, and three different values of $\rho$.
\begin{figure} \epsfxsize =3in \centerline {\epsffile{gvsrho.ps}}\end{figure}

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Jim Keener
2000-09-06